Position control apparatus and disk apparatus using the same

ABSTRACT

According to one embodiment, a position control apparatus includes: a digital control module that performs position control including disturbance adaptive control with a predetermined sampling period using a control constant, in accordance with a position error between a target position and a current position of the object; and a table that stores the control constant corresponding to a value of sin(ωT) or cos(ωT), wherein the digital control module is configured to determine a control value of the actuator in accordance with the position error, calculates the value of sin(ωT) or cos(ωT) according to an adaptive law from a signal based on the position error, reads the corresponding control constant from the table in accordance with the calculated value of sin(ωT) or cos(ωT), and updates the control constant, to perform the position control including the disturbance adaptive control.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of PCT international application Ser.No. PCT/JP2007/000468 filed on Apr. 27, 2007 which designates the UnitedStates, incorporated herein by reference.

BACKGROUND

1. Field

The present invention relates to a position control apparatus and a diskapparatus for preventing displacement of an object due to a disturbance,and more particularly, to a position control apparatus and a diskapparatus for preventing displacement due to an unknown disturbancefrequency.

2. Description of the Related Art

In recent years, devices for performing position control on objects withhigh precision are widely used. For example, in a disk apparatus thatperforms recording and reproduction of data on a rotating storage medium(such as a disk medium) with a head, the head is positioned onto adesired track of the storage medium, and data is read from or written onthe track. In such a disk apparatus as a magnetic disk apparatus or anoptical disk apparatus, it is very important to accurately position ahead onto a target track, so as to achieve higher recording density.

One of the factors that hinder the positioning is the decentering causedwhen the centers of concentric servo signals on a disk differ from therotational center of the motor. To correct the decentering, a controlmethod involving an observer has been suggested (see Japanese Patent(KOKAI) No. 3,460,795, for example).

The decentering leads to sinusoidal position fluctuations that are insynchronization with an integral multiple of the rotation frequency ofthe disk. By the above mentioned observer control method, suchsinusoidal position fluctuations can be restrained, and accuratepositioning on each target track can be performed. However, to performsuch a decentering correction, the frequency to be corrected should beknown in advance. For example, the frequency to be corrected should bean integral multiple of the rotation frequency, or should be equal to ortwice as high as the rotation frequency.

The second factor that hinders the positioning is the vibrationstransmitted from outside the disk apparatus. The vibrations may havevarious waveforms, but in the following, sinusoidal vibrations areexplained. Besides, the above decentering correction control may beapplied for the case with frequencies that are not integral multiples ofthe rotation frequency.

In the above conventional structure, the frequency of a disturbance isof a known value. However, external vibrations transmitted from outsideare unknown at the stage of designing the control system, and thefrequency cannot be known in advance. Therefore, it is necessary todetect unknown frequencies. As long as the frequencies can be detected,position fluctuations due to external vibrations can be prevented (byadaptively following the external vibrations) according to the controlmethod as disclosed in Japanese Patent (KOKAI) No. 3,460,795.

FIG. 15 illustrates the structure of a conventional control system thatdetects a disturbance frequency, and suppresses a sinusoidal disturbanceat a predetermined frequency, so as to perform position followingcontrol. As illustrated in FIG. 15, an arithmetic module 120 calculatesthe position error e between a target position r and the currentposition y, and a control module (Cn) 121 calculates a control amountUn. With this control amount Un, a plant 122 (such as a VCM of a diskapparatus) is driven. In a disk apparatus, servo signals from a magnetichead are demodulated, and the current position y of the plant 122 iscalculated and is fed back to the arithmetic module 120.

An estimator 124 estimates the angular frequency ω of an externalvibration, with the use of the position error e and an internal variableof a disturbance suppression compensator 123 (Cd). A compensation table125 stores constants of the compensator 123 (Cd) for suppressingexternal oscillations at each frequency ω. The disturbance suppressioncompensator 123 (Cd) corrects the internal constant in accordance with aconstant that is read from the compensation table 125 in accordance withthe angular frequency ω of the estimator 124. In this manner, adisturbance suppression control amount Ud is calculated from theposition error e. An addition module 126 adds the control amount Un andthe disturbance suppression control amount Ud, and outputs the additionresult to the plant 122.

As described above, according to a conventional method, the angularfrequency (the disturbance frequency) ω is estimated, and the internalconstant of the compensator Cd is corrected in accordance with the valueof the angular frequency ω. In this manner, an optimum operation of thecompensator Cd is maintained over a wide frequency range (see JapanesePatent Application Publication (KOKAI) No. 2007-004946, for example).

To adapt to unknown disturbance frequencies, the estimated angularfrequency ω is corrected whenever necessary in the conventionalestimation of the angular frequency ω. Therefore, the adaptive law isobtained through an analog control system in the following manner. Therotation vector of the compensator that compensates periodicdisturbances is expressed by the following series of equations (1):

z1=A·cos(ωt),

z2=A·sin(ωt).  1)

In the equations (1), z1 and z2 represent the X-axis component and theY-axis component of the rotation vector.

The following equations (2) are obtained by temporally differentiatingz1 and z2 of the equations (1) with respect to time. Here, ω is functionof time.

$\begin{matrix}{{{\frac{}{t}z\; 1} = {{{- A} \cdot {\sin \left( {\omega \; t} \right)} \cdot \left( {\omega + {\omega^{\prime}t}} \right)} = {{- z}\; {2 \cdot \left( {\omega + {\omega^{\prime \;}t}} \right)}}}},{{\frac{}{t}z\; 2} = {{A \cdot {\cos \left( {\omega \; t} \right)} \cdot \left( {\omega + {\omega^{\prime}t}} \right)} = {z\; {1 \cdot \left( {\omega + {\omega^{\prime}t}} \right)}}}},.} & (2)\end{matrix}$

The angle of the rotation vector is the tangent of the sin component z1and the cos component z2, and the angular frequency ω is thedifferential value of the angle. Accordingly, the angular frequency ω ofthe rotation vector is determined by the following equation (3):

$\begin{matrix}{\frac{\theta}{t} = {{\frac{}{t}\left( {\omega \; t} \right)} = {{\omega + {\omega^{\prime}t}} = {{\frac{}{t}{\tan^{- 1}\left( \frac{z\; 2}{z\; 1} \right)}} = {\frac{{z\; 1\frac{{z}\; 2}{t}} - {\frac{{z}\; 1}{t}z\; 2}}{{z\; 1^{2}} + {z\; 2^{2}}}.}}}}} & (3)\end{matrix}$

Here, the compensator uses the following equation (4). In the equation(4), ω is assumed to be a constant.

$\begin{matrix}{{s\begin{pmatrix}{z\; 1} \\{z\; 2}\end{pmatrix}} = {{\begin{pmatrix}0 & {- \omega} \\\omega & 0\end{pmatrix}\begin{pmatrix}{z\; 1} \\{z\; 2}\end{pmatrix}} + {\begin{pmatrix}{L\; 4} \\{L\; 5}\end{pmatrix}{e.}}}} & (4)\end{matrix}$

In the equation (4), z1 represents the sine component of thedisturbance, z2 represents the cosine component of the disturbance, L4and L5 represent input gains, e represents the position error, and srepresents the Laplacian.

The state equation of the analog compensator of the equation (4) isexpanded, and the differentials of z1 and z2 are determined. Thefollowing equation (5) is obtained by substituting the differentials ofz1 and z2 into the equation (3).

$\begin{matrix}\begin{matrix}{{\omega + {\omega^{\prime}t}} = \frac{{z\; 1\left( {{{\omega \cdot z}\; 1} + {L\; {5 \cdot e}}} \right)} - {\left( {{{{- \omega} \cdot z}\; 2} + {L\; {4 \cdot e}}} \right)z\; 2}}{{z\; 1^{2}} + {z\; 2^{2}}}} \\{= {\omega + {\frac{{L\; {5 \cdot \; z}\; 1} - {L\; {4 \cdot {z2}}}}{{z\; 1^{2}} + {z\; 2^{2}}}{e.}}}}\end{matrix} & (5)\end{matrix}$

If the estimated angular frequency of an unknown disturbance is correct,the compensator 123 (Cd) can properly suppress the disturbance. As aresult, the position error e or the estimated position error of theobserver becomes zero. In other words, when the angular frequency w tobe processed by the compensator 23 (Cd) is the same as the estimatedangular frequency ω of a disturbance, ω′ of the equation (5) or the termof the position error e of the right side should be zero. Accordingly,the equation (5) is expressed by a time differential form of the angularfrequency, to obtain the adaptive law (an integral compensation law)expressed by the following equation (6):

$\begin{matrix}{{\frac{}{t}\omega} = {{K \cdot \frac{{L\; {5 \cdot \; z}\; 1} - {L\; {4 \cdot z}\; 2}}{{z\; 1^{2}} + {z\; 2^{2}}}}{e.}}} & (6)\end{matrix}$

The value of ω is corrected whenever necessary, with the use of thisequation. The equation (6) is transformed into an integral formexpressed by a digital control equation, and the following equation (7)is obtained:

$\begin{matrix}{{\omega \left\lbrack {k + 1} \right\rbrack} = {{\omega \lbrack k\rbrack} + K - {\frac{{L\; {5 \cdot \; z}\; {1\lbrack k\rbrack}} - {L\; {4 \cdot z}\; {2\lbrack k\rbrack}}}{{z\; {1\lbrack k\rbrack}^{2}} + {z\; {2\lbrack k\rbrack}^{2}}}{e.}}}} & (7)\end{matrix}$

Here, K represents the adaptive gain. The equation (7) uses the adaptivelaw in an addition formula. This can be expressed by a multiplicationformula. With the use of this adaptive law, a linear relationship can beobtained between a disturbance oscillation frequency and the estimatedfrequency ω, as illustrated in FIG. 16.

In recent years, the aforementioned control system is applied to adigital control system so as to execute the above control system in dataprocessing of a processor. In the above conventional technique, ananalog adaptive law is obtained based on analog formulas, and the analogadaptive law is converted into a digital adaptive law. As a result, whenthe equation (7) is used in a digital control operation, a disturbancecannot be properly suppressed (or position following cannot be performedwith respect to the disturbance) through digital disturbance adaptivecontrol. This is because the estimated angular frequency ω is based onanalog formulas, though it is directly determined.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

A general architecture that implements the various features of theinvention will now be described with reference to the drawings. Thedrawings and the associated descriptions are provided to illustrateembodiments of the invention and not to limit the scope of theinvention.

FIG. 1 is an exemplary diagram of a disk storage device according to afirst embodiment of the invention;

FIG. 2 is an exemplary explanatory diagram of a positional signal on adisk having the structure of FIG. 1 in the first embodiment;

FIG. 3 is an exemplary explanatory diagram of the positional signal ofFIG. 2 in greater detail in the first embodiment;

FIG. 4 is an exemplary explanatory diagram of a seek operation of a headillustrated in FIG. 1 in the first embodiment;

FIG. 5 is an exemplary block diagram of a position control system havinga disturbance suppression compensator in the first embodiment;

FIG. 6 illustrates a relationship between sin ωT and the oscillationfrequency of FIG. 5;

FIG. 7 illustrates a relationship between cos ωT and the oscillationfrequency of FIG. 5;

FIG. 8 is an exemplary block diagram of a position control system havinga disturbance suppression compensator according to a second embodimentof the invention;

FIG. 9 illustrates an exemplary structure of a table in the structureillustrated in FIG. 8 in the second embodiment;

FIG. 10 is an exemplary diagram of another estimator in the structureillustrated in FIG. 8 in the second embodiment;

FIG. 11 is an exemplary block diagram of a position control systemhaving a disturbance suppression compensator according to a thirdembodiment of the invention;

FIG. 12 illustrates the structure of another sin(ωT) estimator in thestructure of FIG. 11;

FIG. 13 is an exemplary block diagram of a position control systemhaving a disturbance suppression compensator according to a fourthembodiment of the invention;

FIG. 14 is an exemplary block diagram of a position control systemhaving a disturbance suppression compensator according to a fifthembodiment of the invention;

FIG. 15 is an exemplary block diagram of a conventional position controlsystem having a disturbance adaptive control function according to otherembodiments of the invention; and

FIG. 16 is an exemplary explanatory diagram of the conventionaldisturbance frequency estimation in the structure illustrated in FIG. 15in the other embodiments.

DETAILED DESCRIPTION

Various embodiments according to the invention will be describedhereinafter with reference to the accompanying drawings. In general,according to one embodiment of the invention, A position controlapparatus configured to perform position control on an object with theuse of an actuator in accordance with a position of the object,includes: a digital control module configured to perform positioncontrol including disturbance adaptive control with a predeterminedsampling period using a control constant, in accordance with a positionerror between a target position and a current position of the object;and a table configured to store the control constant corresponding to avalue of sin(ωT) or cos(ωT), with ω representing an angular frequency ofa disturbance, T representing the sampling period. The digital controlmodule is configured to determine a control value of the actuator inaccordance with the position error, calculates the value of sin(ωT) orcos(ωT) according to an adaptive law from a signal based on the positionerror, reads the corresponding control constant from the table inaccordance with the calculated value of sin(ωT) or cos(ωT), and updatesthe control constant, to perform the position control including thedisturbance adaptive control.

According to another embodiment of the invention, a disk apparatusincludes: a head configured to read information from a disk; an actuatorconfigured to move the head in a transverse direction of tracks of thedisk; a digital control module configured to perform position controlincluding disturbance adaptive control with a predetermined samplingperiod using a control constant, in accordance with a position errorbetween a target position and a current position of the object; and atable configured to store the control constant corresponding to a valueof sin(ωT) or cos(ωT), with ω representing an angular frequency of adisturbance, T representing the sampling period. The digital controlmodule is configured to determine a control value of the actuator inaccordance with the position error, calculates the value of sin(ωT) orcos(ωT) according to an adaptive law from a signal based on the positionerror, reads the corresponding control constant from the table inaccordance with the calculated value of sin(ωT) or cos(ωT), and updatesthe control constant, to perform the position control including thedisturbance adaptive control.

The following is a description of a disk apparatus, a first embodimentof a position control system, a second embodiment of a control positionsystem, a third embodiment of a position control system, a fourthembodiment of a position control system, a fifth embodiment of aposition control system, and other embodiments, with reference to theaccompanying drawings.

FIG. 1 is a configuration diagram of a disk apparatus according to theembodiments. FIG. 2 is a layout of position signals on a magnetic disk.FIG. 3 is a configuration diagram of position signals on the magneticdisk of FIGS. 1 and 2. FIG. 4 is an explanatory diagram of the headposition control of FIG. 1.

FIG. 1 illustrates a magnetic disk apparatus as the disk apparatus. Asillustrated in FIG. 1, a magnetic disks 4 that are magnetic storagemedium are provided around a rotating shaft 2 of a spindle motor 5. Thespindle motor 5 rotates the magnetic disks 4. An actuator (VCM) 1 hasmagnetic heads 3 at the top ends of its arms, and moves the magneticheads 3 in the radial direction of the magnetic disks 4.

The actuator 1 is formed with a voice coil motor (VCM) that revolvesaround a rotating shaft. In the drawing, the two magnetic disks 4 aremounted on the magnetic disk apparatus, and the four magnetic heads 3are simultaneously driven by the same actuator 1.

Each of the magnetic heads 3 includes a read element and a writeelement. Each of the magnetic heads 3 is formed by stacking the readelement including magnetoresistive (MR) elements on a slider and thewrite element including write coils on the read element.

A position detect circuit 7 converts positional signals (analog signals)read by the magnetic heads 3 into digital signals. A read/write (R/W)circuit 10 controls reading and writing of the magnetic heads 3. Aspindle motor (SPM) drive circuit 8 drives the spindle motor 5. A voicecoil motor (VCM) drive circuit 6 supplies a driving current to the voicecoil motor (VCM) 1, to drive the VCM 1.

A microcontroller (NCU) 14 detects (demodulates) the current positionfrom the digital positional signal supplied from the position detectcircuit 7, and calculates a VCM drive command value in accordance withthe position error of the detected current position and a targetposition. In other words, the MCU 14 performs position demodulation andservo control. A read only memory (ROM) 13 stores the control programfor the MCU 14 and the like. A random access memory (RAM) 12 stores datato be used for the processing by the MCU 14 and the like.

A hard disk controller (HDC) 11 determines a position in a cycle, basedon the sector number of servo signals, and records or reproduces data. Arandom access memory (RAM) 15 for buffering temporarily stores read dataand write data. The HDC 11 communicates with a host via an interface(IF) such as a USB, ATA, or SCSI. A bus 9 connects those components.

As illustrated in FIG. 2, servo signals (positional signals) 16 arecircumferentially arranged at equal intervals on each of the tracks fromthe outer circumference to the inner circumference of each magnetic disk4. Each of the tracks is formed with sectors, and the solid lines inFIG. 2 represent the recorded positions of the servo signals 16. Asillustrated in FIG. 3, each of the positional signals is formed with aservo mark “SERVO MARK”, a track number “GRAY CODE”, an index signal“INDEX”, and offset information (servo bursts) PosA, PosB, PosC, andPosD. The dotted lines in FIG. 3 represent track centers.

With the use of the track number “GRAY CODE” and the offset informationPosA, PosB, PosC, and PosD, the position of the magnetic head in theradial direction is detected. Based on the index signal “INDEX”, theposition of the magnetic head in the circumferential direction isgrasped.

For example, the sector number at which an index signal is detected isset at “0”, and the sector number is incremented every time a servosignal is detected. In this manner, the sector number of each sector ofeach track is obtained. The sector numbers of servo signals are used asthe references when data recording or reproduction is performed. Anindex signal is provided for each one rotation. Instead of the indexsignals, the sector number may be used.

FIG. 4 illustrates an example of seek control to be performed by the MCU14 of FIG. 1 on the actuator. The MCU 14 checks the position of theactuator through the position detect circuit 7 of FIG. 1. The MCU 14performs a servo calculation, and supplies an appropriate current to theVCM 1. FIG. 4 depicts the control transition from the seek startingpoint at which a head 3 is moved from a track position to a target trackposition. FIG. 4 also depicts the current of the actuator 1, thevelocity of the actuator (the head), and the position of the actuator(the head).

The seek control transits to coarse control, to settling control, and tofollowing control, so that the head can be moved to the target position.The coarse control is basically velocity control, and the settlingcontrol and the following control are basically position control. Ineither case, it is necessary to detect the current position of the head.

To check the position, the servo signals are recorded on the magneticdisk in advance, as illustrated in FIG. 2. More specifically, the servemarks representing the starting positions of the servo signals, the graycodes representing the track numbers, the index signals, and signalsPosA through PosD representing offsetting are recorded as illustrated inFIG. 3. Those signals are read by the magnetic heads, and the positiondetect circuit 7 converts the servo signals into digital values.

FIG. 5 is a block diagram of a first embodiment of a position controlsystem (a servo control system). FIG. 6 illustrates the relationshipbetween the oscillation frequency and the estimate value sin(ωT) of FIG.5. FIG. 7 illustrates the relationship between the oscillation frequencyand the estimated value cos(ωT) of FIG. 5.

FIG. 5 is an arithmetic block diagram of the servo control system to berealized by the MCU 14. More specifically, an arithmetic module 20calculates the position error e between a target position r and acurrent position y, and inputs the position error e to a control module(Cn) 21. Based on the position error e, the control module (Cn) 21performs a control operation to calculate a control amount Un and drivethe VCM 1 and 3 that are a plant (P) 22. The position of the plantdemodulates the servo signals from the magnetic heads 3, calculates thecurrent position y, and feeds the current position y back to thearithmetic module 20.

An estimator 24 estimates sin(ωT) with the angular frequency ω ofexternal oscillation, using the position error e and the internalvariable of a disturbance suppression compensator (Cd) 23. A controlvariable table 25 stores the constants of the compensator (Cd) 23 forsuppressing the external oscillation, in association with sin(ωT) withthe angular frequency ω.

The disturbance suppression compensator (Cd) 23 corrects the internalconstant according to the constant read from the compensation table 25,based on the sin(ωT) with the angular frequency ω of the estimator 24.The disturbance suppression compensator (Cd) 23 calculates a disturbancesuppression control amount Ud from the position error e. An additionmodule 26 adds the control amount Un to the disturbance suppressioncontrol amount Ud, and outputs the addition result to the plant 22. Thedisturbance suppression control amount is the amount to be used forcontrolling disturbance in such a manner that the positionalrelationship between the disk and the head is not changed. Since thehead is normally displaced by disturbance, adaptive control is performedon the driving value of the VCM that drives the head.

In the embodiments, the estimator 24 estimates sin(ωT). The reason isdescribed in the following. In the following description, the controlmodule 21, the compensator 23, and the estimator 24 constitute a controlsystem formed with an observer. First, the adaptive law of a predictiveobserver is described.

The compensator 23 in the predictive observer is expressed by thefollowing equation (8). In the equation (8), z1 represents the sinecomponent of the disturbance, z2 represents the cosine component of thedisturbance, L4 and L5 represent input gains, and e represents theposition error.

$\begin{matrix}{\begin{pmatrix}{z\; {1\left\lbrack {k + 1} \right\rbrack}} \\{z\; {2\left\lbrack {k + 1} \right\rbrack}}\end{pmatrix} = {{\begin{pmatrix}{a\; 11} & {a\; 12} \\{a\; 21} & {a\; 22}\end{pmatrix}\begin{pmatrix}{z\; {1\lbrack k\rbrack}} \\{z\; {2\lbrack k\rbrack}}\end{pmatrix}} + {\begin{pmatrix}{L\; 4} \\{L\; 5}\end{pmatrix}{e\lbrack k\rbrack}}}} & (8)\end{matrix}$

If the disturbance model corresponds to a sinusoidal wave, the matrix Aof the equation (8) is expressed by the following equation (9).

$\begin{matrix}{\begin{pmatrix}{a\; 11} & {a\; 12} \\{a\; 21} & {a\; 22}\end{pmatrix} = \begin{pmatrix}{\cos \left( {\omega \; T} \right)} & {- {\sin \left( {\omega \; T} \right)}} \\{\sin \left( {\omega \; T} \right)} & {\cos \left( {\omega \; T} \right)}\end{pmatrix}} & (9)\end{matrix}$

When the equation (8) is expanded, the equation (10) is obtained.

$\begin{matrix}{\begin{pmatrix}{Z_{1}\left\lbrack {k + 1} \right\rbrack} \\{Z_{2}\left\lbrack {k + 1} \right\rbrack}\end{pmatrix} = \begin{pmatrix}{{{a_{11} \cdot Z}\; {1\lbrack k\rbrack}} + {a_{12} \cdot {Z_{2}\lbrack k\rbrack}} + {L_{4} \cdot {e\lbrack k\rbrack}}} \\{{{a_{21} \cdot Z}\; {1\lbrack k\rbrack}} + {a_{22} \cdot {Z_{2}\lbrack k\rbrack}} + {L_{5} \cdot {e\lbrack k\rbrack}}}\end{pmatrix}} & (10)\end{matrix}$

Since the time differential of the equation (2) in analog is asubtraction in digital, the equation (11) is obtained by subtractingZ2[k] from Z2[k+1] of the equation (10), and multiplying the resultantby Z1[k].

z1[k](z2[k+1]−z2[k])=z1[k](a21·z1[k]+(a22−1)z2[k]+L5·e[k])  (11)

Likewise, the equation (12) is obtained by subtracting Z1[k] fromZ1[k+1] of the equation (10), and multiplying the resultant by Z2[k].

z2[k](z1[k+1]−z1[k])=z2[k](a12·z2[k]+(a11−1)z1[k]+L4·e[k])  (12)

Since the analog differentiation is a digital subtraction as in theequation (3), the equation (13) is obtained by determining a differencebetween the equation (11) and the equation (12).

$\begin{matrix}{{{z\; {1\lbrack k\rbrack}\left( {{z\; {2\left\lbrack {k + 1} \right\rbrack}} - {z\; {2\lbrack k\rbrack}}} \right)} - {z\; {2\lbrack k\rbrack}\left( {{z\; {1\left\lbrack {k + 1} \right\rbrack}} - {z\; {1\lbrack k\rbrack}}} \right)}} = {{{z\; {1\lbrack k\rbrack}\left( {{a\; {21 \cdot z}\; {1\lbrack k\rbrack}} + {\left( {{a\; 22} - 1} \right)z\; {2\lbrack k\rbrack}} + {L\; {5 \cdot {e\lbrack k\rbrack}}}} \right)} - {z\; {2\lbrack k\rbrack}\left( {{a\; {12 \cdot z}\; {2\lbrack k\rbrack}} + {\left( {{a\; 11} - 1} \right)z\; {1\lbrack k\rbrack}} + {L\; {4 \cdot {e\lbrack k\rbrack}}}} \right)}} = {{a\; {21 \cdot z}\; {1\lbrack k\rbrack}^{2}} + {\left( {{a\; 22} - {a\; 11}} \right)z\; {{1\lbrack k\rbrack} \cdot z}\; {2\lbrack k\rbrack}} - {a\; {12 \cdot z}\; {2\lbrack k\rbrack}^{2}} + {\left( {{L\; {5 \cdot z}\; {1\lbrack k\rbrack}} - {L\; {4 \cdot z}\; {2\lbrack k\rbrack}}} \right){e\lbrack k\rbrack}}}}} & (13)\end{matrix}$

When the disturbance model corresponds to a sinusoidal wave, thefollowing relationships are satisfied as in the equation (9):a11=a22(=cos(ωT)) and a12=−a22(=sin(ωT)). Accordingly, the equation (13)can be transformed into the following equation (14).

z1[k](z2[k+1]−z2[k])−z2[k](z1[k+1]−z1[k])=sin(ωT)(z1[k] ² +z2[k]²)+(L5−z1[k]−L4·z2[k])e[k]  (14)

The equation (15) is obtained by dividing the equation (14) by the sumof the square of z1 and the square of z2.

$\begin{matrix}{\frac{\begin{matrix}{{z\; {1\lbrack k\rbrack}\left( {{z\; {2\left\lbrack {k + 1} \right\rbrack}} - {z\; {2\lbrack k\rbrack}}} \right)} -} \\{z\; {2\lbrack k\rbrack}\left( {{z\; {1\left\lbrack {k + 1} \right\rbrack}} - {z\; {1\lbrack k\rbrack}}} \right)}\end{matrix}}{{z\; {1\lbrack k\rbrack}^{2}} + {z\; {2\lbrack k\rbrack}^{2}}} = {{\sin \left( {\omega \; T} \right)} + \frac{\begin{pmatrix}{{L\; {5 \cdot z}\; {1\lbrack k\rbrack}} -} \\{L\; {4 \cdot z}\; {2\lbrack k\rbrack}}\end{pmatrix}{e\lbrack k\rbrack}}{{z\; {1\lbrack k\rbrack}^{2}} + {z\; {2\lbrack k\rbrack}^{2}}}}} & (15)\end{matrix}$

Compared with the equation (5), sin(ωT) is estimated as a disturbance inthe equation (15), while ω is estimated as a disturbance in the equation(5). More specifically, in a digital control operation, it is necessaryto estimate sin(ωT), and, according to the adaptive law, sin(ωT) isestimated so that the second term of the right side of the equation (15)becomes “0”.

Next, an adaptive law of a current observer is described. A currentobserver is more widely used than the predictive observer in digitalcontrol.

The compensator 23 in the current observer is expressed by the followingequations (16). In the equations (16), z1 represents the sine componentof the disturbance, z2 represents the cosine component of thedisturbance, L4 and L5 represent input gains, and e represents theposition error.

$\begin{matrix}\left. \begin{matrix}{\begin{pmatrix}{{zh}\; {1\lbrack k\rbrack}} \\{{zh}\; {2\lbrack k\rbrack}}\end{pmatrix} = {\begin{pmatrix}{z\; {1\lbrack k\rbrack}} \\{z\; {2\lbrack k\rbrack}}\end{pmatrix} + {\begin{pmatrix}{L\; 4} \\{L\; 5}\end{pmatrix}{e\lbrack k\rbrack}}}} \\{\begin{pmatrix}{z\; {1\left\lbrack {k + 1} \right\rbrack}} \\{z\; {2\left\lbrack {k + 1} \right\rbrack}}\end{pmatrix} = {\begin{pmatrix}{a\; 11} & {a\; 12} \\{a\; 21} & {a\; 22}\end{pmatrix}\begin{pmatrix}{{zh}\; {1\lbrack k\rbrack}} \\{{zh}\; {2\lbrack k\rbrack}}\end{pmatrix}}}\end{matrix} \right\} & (16)\end{matrix}$

The equation (17) is obtained by combining the two equations (16).

$\begin{matrix}{\begin{pmatrix}{z\; {1\left\lbrack {k + 1} \right\rbrack}} \\{z\; {2\left\lbrack {k + 1} \right\rbrack}}\end{pmatrix} = {{\begin{pmatrix}{a\; 11} & {a\; 12} \\{a\; 21} & {a\; 22}\end{pmatrix}\begin{pmatrix}{z\; {1\lbrack k\rbrack}} \\{z\; {2\lbrack k\rbrack}}\end{pmatrix}} + {\begin{pmatrix}{a\; 11} & {a\; 12} \\{a\; 21} & {a\; 22}\end{pmatrix}\begin{pmatrix}{L\; 4} \\{L\; 5}\end{pmatrix}{e\lbrack k\rbrack}}}} & (17)\end{matrix}$

If the disturbance model corresponds to the sinusoidal wave, the matrixA of the equation (17) is expressed by the following equation (18). Tosimplify the equations, cos(ωT) and sin(ωT) will be hereinafterrepresented by “c” and “s”.

$\begin{matrix}{\begin{pmatrix}{a\; 11} & {a\; 12} \\{a\; 21} & {a\; 22}\end{pmatrix} = {\begin{pmatrix}{\cos \left( {\omega \; T} \right)} & {- {\sin \left( {\omega \; T} \right)}} \\{\sin \left( {\omega \; T} \right)} & {\cos \left( {\omega \; T} \right)}\end{pmatrix} = \begin{pmatrix}c & {- s} \\s & c\end{pmatrix}}} & (18)\end{matrix}$

The inverse matrix of the matrix A of the equation (18) is expressed bythe following equation (19):

$\begin{matrix}{\begin{pmatrix}{a\; 11} & {a\; 12} \\{a\; 21} & {a\; 22}\end{pmatrix}^{- 1} = {\begin{pmatrix}{\cos \left( {\omega \; T} \right)} & {\sin \left( {\omega \; T} \right)} \\{- {\sin \left( {\omega \; T} \right)}} & {\cos \left( {\omega \; T} \right)}\end{pmatrix} = \begin{pmatrix}c & s \\{- s} & c\end{pmatrix}}} & (19)\end{matrix}$

The equation (20) is obtained by dividing the equation (17) by thematrix A of the equation (18), and substituting the inverse matrix ofthe matrix A of the equation (19) into the resultant.

$\begin{matrix}{{\begin{pmatrix}c & s \\{- s} & c\end{pmatrix}\begin{pmatrix}{z\; {1\left\lbrack {k + 1} \right\rbrack}} \\{z\; {2\left\lbrack {k + 1} \right\rbrack}}\end{pmatrix}} = {\begin{pmatrix}{z\; {1\lbrack k\rbrack}} \\{z\; {2\lbrack k\rbrack}}\end{pmatrix} + {\begin{pmatrix}{L\; 4} \\{L\; 5}\end{pmatrix}{e\lbrack k\rbrack}}}} & (20)\end{matrix}$

The equation (21) is obtained by determining z1 and z2 of the k samplefrom the equation (20).

$\begin{matrix}\begin{matrix}{\begin{pmatrix}{z\; {1\lbrack k\rbrack}} \\{z\; {2\lbrack k\rbrack}}\end{pmatrix} = {{\begin{pmatrix}c & s \\{- s} & c\end{pmatrix}\begin{pmatrix}{z\; {1\left\lbrack {k + 1} \right\rbrack}} \\{z\; {2\left\lbrack {k + 1} \right\rbrack}}\end{pmatrix}} - {\begin{pmatrix}{L\; 4} \\{L\; 5}\end{pmatrix}{e\lbrack k\rbrack}}}} \\{= \begin{pmatrix}{{{c \cdot z}\; {1\left\lbrack {k + 1} \right\rbrack}} + {{s \cdot z}\; {2\left\lbrack {k + 1} \right\rbrack}} - {L\; {4 \cdot {e\lbrack k\rbrack}}}} \\{{{{- s} \cdot z}\; {1\left\lbrack {k + 1} \right\rbrack}} + {{c \cdot z}\; {2\left\lbrack {k + 1} \right\rbrack}} - {L\; {5 \cdot {e\lbrack k\rbrack}}}}\end{pmatrix}}\end{matrix} & (21)\end{matrix}$

The equation (22) is obtained by multiplying z1[k] of the equation (21)by z2[k+1], and multiplying z2[k] of the equation (21) by z1[k+1]. Here,the left-side negative sign “−” is given to z2[k].

$\begin{matrix}{\begin{pmatrix}{z\; {1\lbrack k\rbrack}z\; {2\left\lbrack {k + 1} \right\rbrack}} \\{{- z}\; {2\lbrack k\rbrack}z\; {1\left\lbrack {k + 1} \right\rbrack}}\end{pmatrix} = \begin{pmatrix}{{{c \cdot z}\; {1\left\lbrack {k + 1} \right\rbrack}z\; {2\left\lbrack {k + 1} \right\rbrack}} + {{s \cdot z}\; {2\left\lbrack {k + 1} \right\rbrack}^{2}} - {L\; {4 \cdot z}\; {2\left\lbrack {k + 1} \right\rbrack}{e\lbrack k\rbrack}}} \\{{{s \cdot z}\; {1\left\lbrack {k + 1} \right\rbrack}^{2}} - {{c \cdot z}\; {1\left\lbrack {k + 1} \right\rbrack}z\; {2\left\lbrack {k + 1} \right\rbrack}} + {L\; {5 \cdot z}\; {1\left\lbrack {k + 1} \right\rbrack}{e\lbrack k\rbrack}}}\end{pmatrix}} & (22)\end{matrix}$

The equation (23) is obtained by summing up the upper and lower sides ofthe equation (22).

z1[k]z2[k+1]−z2[k]z1[k+1]=s(z1[k+1]²+z2[k+1]²)+(−L4·z2[k+1]+L5·z1[k+1])e[k]  (23)

In the structure of a current observer, sin(ωT) should be estimated fromthe equation (23). More specifically, the disturbance frequency or thedisturbance angular frequency ω that is estimated in an analog operationis not estimated, but sin(ωT) should be directly estimated in a digitalcontrol operation. According to the equation (23), sin(ωT) is obtainedfrom the following equation (24):

$\begin{matrix}{s = {\frac{\begin{matrix}{{z\; {1\lbrack k\rbrack}z\; {2\left\lbrack {k + 1} \right\rbrack}} -} \\{z\; {2\lbrack k\rbrack}z\; {1\left\lbrack {k + 1} \right\rbrack}}\end{matrix}}{{z\; {1\left\lbrack {k + 1} \right\rbrack}^{2}} + {z\; {2\left\lbrack {k + 1} \right\rbrack}^{2}}} + {\frac{\begin{matrix}{{L\; {4 \cdot z}\; {2\left\lbrack {k + 1} \right\rbrack}} -} \\{L\; {5 \cdot z}\; {1\left\lbrack {k + 1} \right\rbrack}}\end{matrix}}{{z\; {1\left\lbrack {k + 1} \right\rbrack}^{2}} + {z\; {2\left\lbrack {k + 1} \right\rbrack}^{2}}}{e\lbrack k\rbrack}}}} & (24)\end{matrix}$

In the current observer, cos(ωT) may be estimated, instead of sin(ωT).More specifically, the equation (25) is obtained by multiplying z1[k] ofthe equation (21) by z1[k+1], and multiplying z2[k] of the equation (21)by z2[k+1].

$\begin{matrix}{\begin{pmatrix}{z\; {1\lbrack k\rbrack}z\; {1\left\lbrack {k + 1} \right\rbrack}} \\{z\; {2\lbrack k\rbrack}z\; {2\left\lbrack {k + 1} \right\rbrack}}\end{pmatrix} = \begin{pmatrix}{{{c \cdot z}\; {1\left\lbrack {k + 1} \right\rbrack}^{2}} + {{s \cdot z}\; {1\left\lbrack {k + 1} \right\rbrack}z\; {2\left\lbrack {k + 1} \right\rbrack}} - {L\; {4 \cdot z}\; {1\left\lbrack {k + 1} \right\rbrack}{e\lbrack k\rbrack}}} \\{{{{- s} \cdot z}\; {1\left\lbrack {k + 1} \right\rbrack}z\; {2\left\lbrack {k + 1} \right\rbrack}} + {{c \cdot z}\; {2\left\lbrack {k + 1} \right\rbrack}^{2}} - {L\; {5 \cdot z}\; {2\left\lbrack {k + 1} \right\rbrack}{e\lbrack k\rbrack}}}\end{pmatrix}} & (25)\end{matrix}$

The equation (26) is obtained by summing up the upper and lower sides ofthe equation (25).

z1[k]z1[k+1]+z2[k]z2[k+1]=c(z1[k+1]²+z2[k+1]²)−(−L4·z1[k+1]−L5·z2[k+1])e[k]  (26)

The disturbance frequency or the disturbance angular frequency ω that isestimated in an analog operation is not estimated, but cos(ωT) should bedirectly estimated in a digital control operation. According to theequation (26), cos(ωT) is obtained from the following equation (27).

$\begin{matrix}{c = {\frac{\begin{matrix}{{z\; {1\lbrack k\rbrack}z\; {1\left\lbrack {k + 1} \right\rbrack}} +} \\{z\; {2\lbrack k\rbrack}z\; {2\left\lbrack {k + 1} \right\rbrack}}\end{matrix}}{{z\; {1\left\lbrack {k + 1} \right\rbrack}^{2}} + {z\; {2\left\lbrack {k + 1} \right\rbrack}^{2}}} - {\frac{\begin{matrix}{{L\; {4 \cdot z}\; {1\left\lbrack {k + 1} \right\rbrack}} +} \\{L\; {5 \cdot z}\; {2\left\lbrack {k + 1} \right\rbrack}}\end{matrix}}{{z\; {1\left\lbrack {k + 1} \right\rbrack}^{2}} + {z\; {2\left\lbrack {k + 1} \right\rbrack}^{2}}}{e\lbrack k\rbrack}}}} & (27)\end{matrix}$

FIG. 6 illustrates the relationship between the oscillation frequencyand the estimated value sin(ωT). The solid line represents the estimatedvalue sin(ωT), and the dot-and-dash line represents the conventionalestimated value ω. Relative to the oscillation frequency represented bythe abscissa axis, the conventional estimated value ω exhibits linearcharacteristics. Compared with the estimated value sin(ωT), theconventional estimated value ω has a difference in estimated frequencywith respect to the oscillation frequency, and the estimation accuracyof the conventional estimated value ω is low. Therefore, in a digitalcontrol operation, the oscillation frequency cannot be accuratelyestimated by estimating the estimated value ω, and position controladapting to the oscillation frequency is difficult.

In the first embodiment, on the other hand, the oscillation frequency isestimated through sin(ωT). Accordingly, in the digital control, theoscillation frequency can be accurately estimated, and position controladapting to the oscillation frequency component can be performed.

Where sin(ωT) is used as the estimated value of the oscillationfrequency f in the digital control, the frequency expressed by thefollowing equation (28) is estimated, with Fs representing the samplingfrequency in the digital control.

$\begin{matrix}{{\sin \left( {\omega \; T} \right)} = {\sin \left( {2\; {\pi \cdot \frac{f}{Fs}}} \right)}} & (28)\end{matrix}$

As illustrated in FIG. 6, a monotonous relationship is observed betweenthe disturbance frequency f and sin(ωT) in the region between 0 andFs/4, and adaptive following cannot be performed where the oscillationfrequency is Fs/4 or higher.

FIG. 7 illustrates the relationship between the oscillation frequencyand the estimated value cos(ωT). As illustrated in FIG. 7, where cos(ωT)is used as the estimated value, a monotonous decrease is obtained in theregion between and Fs/2. Accordingly, there is not a limit at Fs/4 thatis set in the case where sin(ωT) is used as the estimated value.

Where cos(ωT) is used, the curve becomes almost flat in the lowfrequency zone, and the frequency estimation accuracy becomes poorer.For example, in a case of a sample frequency of 12 kHz, the curve isflat in the low frequency zone around 500 Hz, and the estimationaccuracy becomes lower.

Accordingly, sin(ωT) should be used as the estimated value wherepriority is put on the estimation accuracy on the lower frequency side,and cos(ωT) should be used as the estimated value where priority is puton the estimation accuracy on the higher frequency side.

Furthermore, when the disk apparatus is in use, external oscillationsoften become a problem on the lower frequency side. For example,external oscillations of several hundreds Hz are often caused fromoutside. Therefore, in the disk apparatus, it is more convenient to usethe estimated value sin(ωT), with which lower frequency oscillations canbe estimated with higher accuracy.

The estimator 24 of FIG. 5 estimates sin(ωT) or cos(ωT), and performsadaptive control in the following manner.

In a first adaptive control operation, e[k] of the equation (24) or theequation (27) becomes “0”, if accurate estimation is performed, and thecontrol system can suppress the disturbance frequency. Accordingly, thesecond term of the right side of each of the equations (24) and (27)should become “0”.

Therefore, where sin(ωT) is estimated, the second term E[k] of the rightside of the equation (24) is calculated according to the followingequation (29).

$\begin{matrix}{{E\lbrack k\rbrack} = {\frac{{L\; {4 \cdot z}\; {2\left\lbrack {k + 1} \right\rbrack}} - {L\; {5 \cdot z}\; {1\left\lbrack {k + 1} \right\rbrack}}}{{z\; {1\left\lbrack {k + 1} \right\rbrack}^{2}} + {z\; {2\left\lbrack {k + 1} \right\rbrack}^{2}}}{e\lbrack k\rbrack}}} & (29)\end{matrix}$

Next, E[k] of the equation (29) is multiplied by the adaptive gain K, sothat sin(ωT) is updated as in the following equation (30).

sin(ω)[k+1]T)=sin(ω[k]T)+K·E[k]  (30)

Where cos(ωT) is estimated, the second term E[k] of the right side ofthe equation (27) is calculated according to the following equation(31).

$\begin{matrix}{{E\lbrack k\rbrack} = {{- \frac{{L\; {4 \cdot z}\; {1\left\lbrack {k + 1} \right\rbrack}} + {L\; {5 \cdot z}\; {2\left\lbrack {k + 1} \right\rbrack}}}{{z\; {1\left\lbrack {k + 1} \right\rbrack}^{2}} + {z\; {2\left\lbrack {k + 1} \right\rbrack}^{2}}}}{e\lbrack k\rbrack}}} & (31)\end{matrix}$

Next, E[k] of the equation (31) is multiplied by the adaptive gain K, sothat cos(ωT) is updated as in the following equation (32).

cos(ω[k+1]T)=cos(ω[k]T)+K·E[k]  (32)

In the above described manner, sin(ωT) and cos(ωT) can be adaptivelyestimated with the use of the five values, z1[k+1], z2[k+1], e[k], L4,and L5.

A calculation in a second adaptive control operation is now described.Where a fixed-point processor is used, the number of digits is limited.If the above five values, z1[k+1], z2[k+1], e[k], L4, and L5, are used,the number of digits in each of the values of z1[k+1] and z2[k+1]differs from the number of digits in each of the values of e[k], L4, andL5. To effectively use the limited number of digits, calculations areperformed in the following manner.

Where sin(ωT) is estimated, the first term G[k] of the right side of theequation (24) is calculated according to the following equation (33).

$\begin{matrix}{{G\lbrack k\rbrack} = \frac{{z\; {1\lbrack k\rbrack}z\; {2\left\lbrack {k + 1} \right\rbrack}} - {z\; {2\lbrack k\rbrack}z\; {1\left\lbrack {k + 1} \right\rbrack}}}{{z\; {1\left\lbrack {k + 1} \right\rbrack}^{2}} + {z\; {2\left\lbrack {k\; + 1} \right\rbrack}^{2}}}} & (33)\end{matrix}$

The difference E[k] between the current set value sin(ωT) and theequation (33) is calculated according to the following equation (34).

E[k]=G[k]−sin(ω[k]T)  (34)

E[k] of the equation (34) is multiplied by the adaptive gain K, so thatsin(ωT) is updated as in the following equation (35).

sin(ω[k+1]T)=sin(ω[k]T)+K·E[k]  (35)

Where cos(ωT) is estimated, the first term G[k] of the right side of theequation (27) is calculated according to the following equation (36):

$\begin{matrix}{{G\lbrack k\rbrack} = \frac{{z\; {1\lbrack k\rbrack}z\; {1\left\lbrack {k + 1} \right\rbrack}} + {z\; {2\lbrack k\rbrack}z\; {2\left\lbrack {k + 1} \right\rbrack}}}{{z\; {1\left\lbrack {k + 1} \right\rbrack}^{2}} + {z\; {2\left\lbrack {k\; + 1} \right\rbrack}^{2}}}} & (36)\end{matrix}$

The difference E[k] between the current set value cos(ωT) and theequation (36) is calculated according to the following equation (37).

E[k]=G[k]−cos(ω[k]T)  (37)

E[k] of the equation (37) is multiplied by the adaptive gain K, so thatcos(ωT) is updated as in the following equation (38).

cos(ω[k+1]T)=cos(ω[k]T)+K·E[k]  (38)

In the above described manner, sin(ωT) and cos(ωT) can be adaptivelyestimated only with the use of the four values, z1[k+1], z1[k], z2[k+1],and z2[k].

The compensator 23 illustrated in FIG. 5 is formed with an observer, andcalculates the disturbance suppression control amount (current) Udist(or Ud) according to the following equation (39):

$\begin{matrix}{{\begin{pmatrix}{Z\; {1\left\lbrack {k + 1} \right\rbrack}} \\{Z\; {2\left\lbrack {k + 1} \right\rbrack}}\end{pmatrix} = {{H\begin{pmatrix}{Z\; {1\lbrack k\rbrack}} \\{Z\; {2\lbrack k\rbrack}}\end{pmatrix}} + {\begin{pmatrix}L_{4} \\L_{5}\end{pmatrix}{e\lbrack k\rbrack}}}},{{{Udist}\lbrack k\rbrack} = {F \cdot \begin{pmatrix}{Z\; {1\lbrack k\rbrack}} \\{Z\; {2\lbrack k\rbrack}}\end{pmatrix}}},{H = \begin{pmatrix}{\cos \left( {{\omega \lbrack k\rbrack}T} \right)} & {- {\sin \left( {{\omega \lbrack k\rbrack}T} \right)}} \\{\sin \left( {{\omega \lbrack k\rbrack}T} \right)} & {\cos \left( {{\omega \lbrack k\rbrack}T} \right)}\end{pmatrix}}} & (39)\end{matrix}$

The control variable table 25 of FIG. 5 stores the values of sin(ωT) orcos(ωT) to be used in the equation (39), and the corresponding values ofL4, L5, and cos(ωT) or sin(ωT), as illustrated in FIG. 9.

Accordingly, for each sample, the values of L4, L5, and cos(ωT) orsin(ωT) corresponding to sin(ωT) or cos(ωT) calculated by the estimator24 are read from the control variable table 25, and are set into thecompensator 23. Based on the set control constants and the positionerror, the compensator 23 calculates the disturbance suppression controlamount Udist according to the equation (39), and outputs the disturbancesuppression control amount Udist to the addition module 26.

Accordingly, where position control adapting to a disturbance frequencyis performed in a digital position control system, the oscillationfrequency is accurately estimated, so that position control adapting tothe oscillation frequency component can be performed.

FIG. 8 is a block diagram of a position control system of a secondembodiment. FIG. 9 is an explanatory diagram of the control variabletable of FIG. 8. The structure illustrated in FIG. 8 is an example inwhich the controller 21 and the compensator 23 are formed with anintegral current observer. Also, in this example, the estimator 24utilizes the calculation method of the first adaptive control.

The position control system of FIG. 8 is a current observer thatperforms disturbance suppression expressed by the following equations(40), (41), and (42), so as to detect the disturbance frequency andsuppress disturbance through adaptive control.

$\begin{matrix}{\begin{pmatrix}{x(k)} \\{v(k)} \\{b(k)} \\{z\; 1(k)} \\{z\; 2(k)}\end{pmatrix} = {\begin{pmatrix}{x(k)} \\{v(k)} \\{b(k)} \\{z\; 1(k)} \\{z\; 2(k)}\end{pmatrix} + {\begin{pmatrix}{L\; 1} \\{L\; 2} \\{L\; 3} \\{L\; 4} \\{L\; 5}\end{pmatrix}\left( {{y(k)} - {x(k)}} \right)}}} & (40) \\{{u(k)} = {{- \left( {F\; 1\mspace{14mu} F\; 2\mspace{14mu} F\; 3\mspace{14mu} F\; 4\mspace{14mu} F\; 5} \right)}\begin{pmatrix}{x(k)} \\{v(k)} \\{b(k)} \\{z\; 1(k)} \\{z\; 2(k)}\end{pmatrix}}} & (41) \\{\begin{pmatrix}{x\left( {k + 1} \right)} \\{v\left( {k + 1} \right)} \\{b\left( {k + 1} \right)} \\{z\; 1\left( {k + 1} \right)} \\{z\; 2\left( {k + 1} \right)}\end{pmatrix} = {{\begin{pmatrix}1 & 1 & {1/2} & {1/2} & 0 \\0 & 1 & 1 & 1 & 0 \\0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & {a\; 11} & {a\; 21} \\0 & 0 & 0 & {a\; 21} & {a\; 22}\end{pmatrix} \begin{pmatrix}{x(k)} \\{v(k)} \\{b(k)} \\{z\; 1(k)} \\{z\; 2(k)}\end{pmatrix}} + {\frac{B\; 1}{m}\frac{1}{Lp}{T^{2}\begin{pmatrix}{1/2} \\1 \\0 \\0 \\0\end{pmatrix}}{u(k)}}}} & (42)\end{matrix}$

In the equation (42), a11 through a22 represent the values of sine andcosine in the equations (9) and (18).

In other words, the second embodiment is an example of a positioncontrol system that is formed with an observer involving a controllermodel and a disturbance model. In FIG. 8, the same components and partsas those illustrated in FIG. 5 are denoted by the same referencenumerals and symbols as those used in FIG. 5.

In FIG. 8, the first arithmetic module 20 subtracts the target positionr from an observed position y[k] obtained by demodulating the abovedescribed servo information read by the head 3 (see FIG. 1), todetermine an actual position error er[k].

A second arithmetic module 32 subtracts an estimated position x[k] ofthe observer from the actual position error er[k], to determine anestimated position error e[k]. A state estimating module 34 uses theestimated position error e[k] and the estimated gains L (L1, L2, L3, L4,and L5) as interval variables of the equation (40), to determineestimated correction values (the second term of the right side of theequation (40)).

An addition module 36 adds the estimated correction value to the statequantities from a delay module 46 (the first terms of the right side ofthe equation (40)) x[k], v[k], b[k], z1[k], and z2[k], so as todetermine an estimated position x[k], an estimated velocity v[k], anestimated bias value b[k], and estimated disturbance suppression valuesz1[k] and z2[k] as in the equation (40). In the equation (40), theestimated position error e[k] is represented by (y[k]−x[k]).

The estimated values are multiplied by a state feedback gain (−Fa=F1,F2, F3, F4, and F5) at a fourth arithmetic module 38, to obtain thedriving value u[k] of the actuator 1, as in the equation 41. Meanwhile,the estimated value of the equation (40) from the addition module 36 ismultiplied by an estimated gain Aa (the matrix of the first term of theright side of the equation (42)) at a fifth arithmetic module 42.

The driving value u[k] of the fourth arithmetic module 38 is multipliedby an estimated gain B (by which u [k] of the second term of the rightside of the equation (42) is multiplied) at a sixth arithmetic module40. The two multiplication results are added to each other at anaddition module 44, to obtain estimated state quantities x[k+1], v[k+1],b[k+1], z1[k+1], and z2[k+1] of the next sample of the equation (42).

As described above, the estimated state quantities of the next samplesare input to the delay module 46, and are corrected with the estimatedcorrection values at the state estimating module 34. At a seventharithmetic module 48, the estimated position x[k] is extracted from theestimated value of the equation (41) from the addition module 36, and isinput to the second arithmetic module 32.

The estimator 24 and the control variable table 25 are given to thecurrent observer. The estimator 24 calculates sin(ωT) according to theequations (29) and (30), which are the first adaptive law of sin(ωT).More specifically, in the estimator 24, an estimated error (E[k])calculator 24-1 receives the estimated position error e[k], theestimated state quantities z1[k+1] and z2[k+1], and the estimated gainsL4 and L5. According to the equation (29), the estimated errorcalculator 24-1 calculates and outputs an estimated error E[k].

Again multiplier 24-2 multiplies the estimated error E[k] by a gain Ka,and calculates the second term of the right side of the equation (30).An adder 24-4 adds sin(ω[k]T) of the previous sample from a delay module24-3 to the output of the gain multiplier 24-2, and outputs sin(ω[k+1]T)of the equation (30). The sin(ω[k+1]T) is delayed by one sample at thedelay module 24-3, and is input to the adder 24-5.

The output sin(ω[k+1]T) of the frequency estimator 24 is input to thecontrol variable table 25. As illustrated in FIG. 9, the controlvariable table 25 stores the values of the estimated gains L1, L2, L3,L4, and L5, and the values of cos(ωT) corresponding to the estimatedvalues of sin(ωT). As illustrated in FIG. 6, the region of 0 to Fs/4 isused. Therefore, in the table illustrated in FIG. 9, thirty-three valuesof sin(ωT) are allotted within the range of 0 to Fs/4.

The control variable table 25 extracts the estimated gain L and cos(ωT)corresponding to the estimated value sin(ωT), and sets the extractedvalues in the modules 34 and 42. In this manner, the estimated gains L1through L5 of the equation (40) of the module 34 and the controlconstants a11 through a22 (=cos(ωT) or sin(ωT)) of the equation (42) ofthe module 42 are updated, and the disturbance suppressioncharacteristics of the observer are changed in accordance with thedisturbance frequency.

As described above, where a current observer is used, designing is easy,and the disturbance suppression function can be readily set. Also, in acase where the frequency estimator 24 estimates cos(ωT), thecalculations can be performed with the same structure as above.

FIG. 10 is a block diagram of another frequency estimator 24 in thestructure illustrated in FIG. 8. In FIG. 10, the same components andparts as those in FIG. 8 are denoted by the same reference numerals andsymbols as those used in FIG. 8.

As described above, the values of sin(ωT) corresponding to the frequencyrange of 0 to Fs/4 fall into the range of 0 to 1. Therefore, theestimated value of sin(ωT) needs to be always restricted within therange of 0 to 1. In the embodiment, a clip module 24-5 is provided torestrict the output of the addition module 24-4 within the range of 0 to1.

If the input sin(ωT) is smaller than “0”, a clip module (a saturationprocessing module) 24-5 restricts sin(ωT) to “0”. If the input sin(ωT)is larger than “1”, the clip module 24-5 restricts sin(ωT) to “1”.Accordingly, even if sin(ωT) is estimated from the state variables, adisturbance frequency component within the frequency range illustratedin FIG. 6 can be obtained.

Where cos(ωT) is estimated, the same effects as above can be achieved byrestricting the clipping range to “−1” to “+1”.

FIG. 11 is a block diagram of a position control system of a thirdembodiment. The structure illustrated in FIG. 11 is an example in whichthe controller 21 and the compensator 23 are formed with an integralcurrent observer. Also, in this example, a sin(ωT) estimator 24Autilizes the calculation method of the second adaptive control.

In FIG. 11, the same components and parts as those illustrated in FIG. 8are denoted by the same reference numerals and symbols as those used inFIG. 8. Like the position control system of FIG. 8, the position controlsystem of FIG. 11 is a current observer involving the bias compensationexpressed by the above equations (40), (41), and (42), so as to suppressa disturbance by detecting the disturbance frequency and performingadaptive control. Therefore, explanation of the current observers 21,23, and 26 is omitted herein.

As illustrated in FIG. 11, the frequency estimator 24A and the controlvariable table 25 are given to the current observer. The frequencyestimator 24A calculates sin(ωT) according to the equations (33) through(35), which is the second adaptive law of sin(ωT). More specifically, inthe frequency estimator 24A, an estimated error calculator 24-6 receivesthe estimated state quantities z1[k], z1[k+1], z2[k], and z2[k+1].According to the equation (33), the estimated error calculator 24-6calculates and outputs a first estimated error G[k].

A first arithmetic module 24-7 subtracts sin(ω[k]T) of one previoussample supplied from a delay module 24-9 from the first estimated errorG[k], and outputs a second estimated error E[k] of the equation (34).

A gain multiplier 24-8 multiplies the second estimated error E[k] by again K, and calculates the second term of the right side of the equation(35). An adder 24-10 adds sin(ω[k]T) of the previous sample from thedelay module 24-9 to the output of the gain multiplier 24-S, and outputsthe sin(ω[k+1]T) of the equation (35). The sin(ω[k+1]T) is delayed byone sample at the delay module 24-9, and is input to the arithmeticmodule 24-7 and the adder 24-10.

The output sin(ω[k+1]T) of the frequency estimator 24A is input to thecontrol variable table 25. As illustrated in FIG. 9, the controlvariable table 25 stores the values of the estimated gains L1, L2, L3,L4, and L5, and the values cos(ωT) corresponding to estimated valuessin(ωT). As illustrated in FIG. 6, the region of 0 to Fs/4 is used forsin(ωT). Therefore, in the table illustrated in FIG. 9, thirty-threevalues of sin(ωT) are allotted within the range of 0 to Fs/4.

The control variable table 25 extracts the estimated gain L and cos(ωT)corresponding to the estimated value sin(ωT), and sets the extractedvalues in the modules 34 and 42. In this manner, the estimated gains L1through L5 of the equation (40) of the module 34 and the controlconstants a11 through a22 (=cos(ωT) or sin(ωT)) of the equation (42) ofthe module 42 are updated, and the disturbance suppressioncharacteristics of the observer are changed in accordance with thedisturbance frequency.

As described above, where a current observer is used, designing is easy,and the disturbance suppression function can be readily set. Since thesecond adaptive law is used, there is not a difference in the number ofdigits among inputs. Even if a fixed-point processor is used,calculations can be performed with high precision. Further, where thefrequency estimator 24A estimates cos(ωT), the equations (36) through(38) can be calculated with the same structure as above.

FIG. 12 is a block diagram of another embodiment of the frequencyestimator 24A of FIG. 11. In FIG. 12, the same components and parts asthose in FIGS. 8, 10, and 11 are denoted by the same reference numeralsand symbols as those used in FIGS. 8, 10, and 11.

As described above, the values of sin(ωT) corresponding to the frequencyrange of 0 to Fs/4 fall into the range of “0” to “1”. Therefore, theestimated value of sin(ωT) needs to be always restricted within therange of “0” to “1”. In the embodiment, a clip module 24-11 thatrestricts the output of the addition module 24-10 within the range of“0” to “1” is provided in the same structure as that illustrated in FIG.11.

If the input sin(ωT) is smaller than “0”, the clip module (a saturationprocessing module) 24-11 restricts sin(ωT) to “0”. If the input sin(ωT)is larger than “1”, the clip module 24-11 restricts sin(ωT) to “1”.Accordingly, if sin(ωT) is estimated from a state variable, adisturbance frequency component within the frequency range of FIG. 6 canbe obtained.

Where cos(ωT) is estimated, the same effects as above can be achieved byrestricting the clipping range to “−1” to “+1”.

FIG. 13 is a block diagram of a position control system of a fourthembodiment. The structure illustrated in FIG. 13 is an example in whichthe controller 21 and the compensator 23 are formed with separatecurrent observers. Also, in the forth embodiment, the estimator 24utilizes the calculation method of the first adaptive control.

The position control system of FIG. 13 is a current observer thatperforms disturbance suppression expressed by the following equations(43), (44), (45), (46), and (47), by detecting the disturbance frequencyand suppressing disturbances through adaptive control.

$\begin{matrix}{\begin{pmatrix}{x(k)} \\{v(k)} \\{b(k)} \\{z\; 1(k)} \\{z\; 2(k)}\end{pmatrix} = {\begin{pmatrix}{x(k)} \\{v(k)} \\{b(k)} \\{z\; 1(k)} \\{z\; 2(k)}\end{pmatrix} + {\begin{pmatrix}{L\; 1} \\{L\; 2} \\{L\; 3} \\{L\; 4} \\{L\; 5}\end{pmatrix}\left( {{y(k)} - {x(k)}} \right)}}} & (43) \\{{u(k)} = {{- \left( {F\; 1\mspace{14mu} F\; 2} \right)}\begin{pmatrix}{x(k)} \\{v(k)}\end{pmatrix}}} & (44) \\{{{uout}(k)} = {{u(k)} - {\left( {F\; 3\mspace{14mu} F\; 4\mspace{14mu} F\; 5} \right)\begin{pmatrix}{b(k)} \\{z\; 1(k)} \\{z\; 2(k)}\end{pmatrix}}}} & (45) \\{\begin{pmatrix}{x\left( {k + 1} \right)} \\{v\left( {k + 1} \right)}\end{pmatrix} = {{\begin{pmatrix}1 & 1 \\0 & 1\end{pmatrix}\begin{pmatrix}{x(k)} \\{v(k)}\end{pmatrix}} + {\frac{B\; 1}{m}\frac{1}{Lp}{T^{2}\begin{pmatrix}{1/2} \\1\end{pmatrix}}{u(k)}}}} & (46) \\\left. \begin{matrix}{{b\left( {k + 1} \right)} = {b(k)}} \\{\begin{pmatrix}{z\; 1\left( {k + 1} \right)} \\{z\; 2\left( {k + 1} \right)}\end{pmatrix} = {\begin{pmatrix}{a\; 11} & {a\; 12} \\{a\; 21} & {a\; 22}\end{pmatrix}\begin{pmatrix}{z\; 1(k)} \\{z\; 2(k)}\end{pmatrix}}}\end{matrix} \right\} & (47)\end{matrix}$

In the equation (47), a11 through a22 represent the values of sine andcosine of the equations (9) and (18).

In other words, the fourth embodiment is an example of a positioncontrol system that is formed with observers including a controllermodel and a disturbance model. In FIG. 13, the same components and partsas those illustrated in FIGS. 5, 8, and 11 are denoted by the samereference numerals and symbols as those used in FIGS. 5, 8, and 11.

In FIG. 13, a first arithmetic module 20 subtracts a target position rfrom an observed position y[k] obtained by demodulating the abovedescribed servo information read by a head 3 (see FIG. 1), to determinean actual position error er[k].

A second arithmetic module 32 subtracts an estimated position x[k] ofthe observer from the actual position error er[k] to determine anestimated position error e[k]. A state estimating module 34-1 uses theestimated position error e[k] and the estimated gains L (L1 and L2) asinterval variables of the equation (43), to determine estimatedcorrection values (the second term of the right side of the equation(43)).

An addition module 36-1 adds the estimated correction value to the statequantities x[k] and v[k] from a delay module 46-1 (the first terms ofthe right side of the equation (40)), so as to determine an estimatedposition x[k] and an estimated velocity v[k], as in the equation (43).In the equation (43), the estimated position error e[k] is representedby (y[k]−x[k]).

The estimated values are multiplied by state feedback gains (−Fa=F1 andF2) at a third arithmetic module 38-1, to obtain the driving value u[k]of the actuator 1, as in the equation (44). Meanwhile, the estimatedvalue of the equation (43) from the addition module 36-1 is multipliedby an estimated gain Aa (the matrix of the first term of the right sideof the equation (46)) at a fourth arithmetic module 42-1.

The driving value u[k] of the third arithmetic module 38-1 is multipliedby an estimated gain B (by which u[k] of the second term of the rightside of the equation (46) is multiplied) at a fifth arithmetic module40. The two multiplication results are added to each other at anaddition module 44, to obtain estimated state quantities x[k+1] andv[k+1] of the next sample of the equation (46).

As described above, the estimated state quantities of the next samplesare input to the delay module 46-1, and are corrected with the estimatedcorrection values at the state estimating module 34-1. At a sixtharithmetic module 48, the estimated position x[k] is extracted from theestimated value of the equation (46) from the addition module 36-1, andis input to the second arithmetic module 32.

Likewise, in the disturbance model, a second state estimating module34-2 uses the estimated position error e[k] and the estimated gains Ld1(L3, L4, and L5) as interval variables of the equation (43), todetermine estimated correction values (the second term of the right sideof the equation (43)).

A second addition module 36-2 adds the estimated correction values tothe state quantities b[k], z1[k], and z2[k] from a second delay module46-2 (the first terms of the right side of the equation (40)), so as todetermine an estimated bias b[k] and estimated disturbance quantitiesz1[k] and z2[k] as the equation (43).

The estimated values are multiplied by state feedback gains (−Fd1=F3,F4, and F5) at a seventh arithmetic module 38-2, to obtain thedisturbance suppression driving value ud[k] of the actuator 1, as in theequation (45). Meanwhile, the estimated value of the equation (43) fromthe second addition module 36-2 is multiplied by an estimated gain Ad1(the matrix of the right side of the equation (47)) at an eightharithmetic module 42-2.

A ninth arithmetic module 50 adds the driving value ud[k] of the seventharithmetic module 38-2 to the driving value u[k] of the third arithmeticmodule 38-1, and outputs the driving value u[k] of the actuator.

In fourth embodiment, the frequency estimator 24 and the controlvariable table 25 are also given to the current observers. The frequencyestimator 24 is the same as that illustrated in FIGS. 8 and 10. Thecontrol variable table 25 is the same as that illustrated in FIG. 9.

The control variable table 25 sets the estimated gains L1 and L2corresponding to the estimated value sin(ωT) in the state estimatingmodule 34-1, and sets the estimated gains L3, L4, and L5, and cos(ωT) inthe modules 34-2 and 42-2. In this manner, the estimated gains L1through L5 of the equation (43) of the modules 34-1 and 34-2, and thecontrol constants a11 through a22 (=cos(ωT) or sin(ωT)) of the equation(47) of the module 42-2 are updated, and the disturbance suppressioncharacteristics of the observers are changed in accordance with thedisturbance frequency.

As described above, where a disturbance model is formed with anindependent current observer, the designing of the disturbance model iseasy, and the disturbance suppression function can be readily set. Also,where the frequency estimator 24 estimates cos(ωT), calculations can beperformed with the same structure as above.

FIG. 14 is a block diagram of a position control system of a fifthembodiment. The structure illustrated in FIG. 14 is an example in whichthe controller 21 and the compensator 23 are formed with separatecurrent observers. Also, in the fifth embodiment, the estimator 24Autilizes the calculation method of the second adaptive control.

In FIG. 14, the same components and parts as those illustrated in FIGS.11 and 13 are denoted by the same reference numerals and symbols asthose used in FIGS. 11 and 13. The position control system of FIG. 14 isa current observer that performs disturbance suppression expressed bythe above equations (43), (44), (45), (46), and (47), so as to detectthe disturbance frequency and suppress disturbance through adaptivecontrol.

In other words, the fifth embodiment is an example of a position controlsystem that is formed with observers including a controller model and adisturbance model, like the example illustrated in FIG. 13. Therefore,explanation of the observers is omitted herein.

In the fifth embodiment, the frequency estimator 24A and the controlvariable table 25 are also given to the current observers. The frequencyestimator 24A is the same as that illustrated in FIGS. 11 and 12. Thecontrol variable table 25 is the same as that illustrated in FIG. 9.

The control variable table 25 sets the estimated gains L1 and L2corresponding to the estimated value sin(ωT) in the state estimatingmodule 34-1, and sets the estimated gains L3, L4, and L5, and cos(ωT) inthe modules 34-2 and 42-2. In this manner, the estimated gains L1through L5 of the equation (47) of the modules 34-1 and 34-2, and thecontrol constants a11 through a22 (=cos(ωT) or sin(ωT)) of the equation(47) of the module 42-2 are updated, and the disturbance suppressioncharacteristics of the observers are changed in accordance with thedisturbance frequency.

As described above, where a disturbance model is formed with anindependent current observer, the designing of the disturbance model iseasy, and the disturbance suppression function can be readily set. Also,where the frequency estimator 24A estimates cos(ωT), calculations can beperformed with the same structure as above.

In the above descriptions, the compensator 23 is formed with anobserver. However, the compensator 23 of FIG. 5 may be formed with afilter. The following is a description of the adaptive law implementedin that case. First, where a filter is used, a filter that corrects theinput gains L is used, and the equations on which the correction isbased are the same as the equation (8) and the following equations of apredictive observer.

The upper side of the equation (10) is multiplied by z2[k], and thelower side of the equation (10) is multiplied by −z1[k], to obtain thefollowing equation (48).

$\begin{matrix}{\begin{pmatrix}{z\; {2\lbrack k\rbrack}z\; {1\left\lbrack {k + 1} \right\rbrack}} \\{z\; {1\lbrack k\rbrack}z\; {2\left\lbrack {k + 1} \right\rbrack}}\end{pmatrix} = \begin{pmatrix}{{{c \cdot z}\; {1\lbrack k\rbrack}z\; {2\lbrack k\rbrack}} - {{s \cdot z}\; {2\lbrack k\rbrack}^{2}} + {L\; {4 \cdot z}\; {2\lbrack k\rbrack}{e\lbrack k\rbrack}}} \\{{{{- s} \cdot z}\; {1\lbrack k\rbrack}^{2}} - {{c \cdot z}\; {1\lbrack k\rbrack}z\; {2\lbrack k\rbrack}} - {L\; {5 \cdot z}\; {1\lbrack k\rbrack}{e\lbrack k\rbrack}}}\end{pmatrix}} & (48)\end{matrix}$

In the equation (48), a11 through a22 of the equation (10) aresubstituted by sine and cosine of the equations (9) and (18), and sineand cosine are represented by “s” and “c”, respectively.

By summing up the upper side and the lower side of the equation (48),the following equation (49) is obtained.

z2[k]z1[k+1]−z1[k]z2[k+1]=−s(z1[k] ² +z2[k]²)+(L4·z2[k]−L5·z1[k])e[k]  (49)

Based on the equation (49), sin(ωT) (=s) is calculated according to thefollowing equation (50).

$\begin{matrix}{s = {\frac{{{z\; {1\lbrack k\rbrack}z\; {2\left\lbrack {k + 1} \right\rbrack}} - {z\; {2\lbrack k\rbrack}z\; {1\left\lbrack {k + 1} \right\rbrack}}}\;}{{z\; {1\lbrack k\rbrack}^{2}} + {z\; {2\lbrack k\rbrack}^{2}}} + {\frac{{L\; {4 \cdot z}\; {2\lbrack k\rbrack}} - {L\; {5 \cdot z}\; {1\lbrack k\rbrack}}}{{z\; {1\lbrack k\rbrack}^{2}} + {z\; {2\lbrack k\rbrack}^{2}}}{e\lbrack k\rbrack}}}} & (50)\end{matrix}$

The equation (50) is set as the adaptive law of the sin(ωT) estimator 24of FIG. 5.

Next, cos(ωT) estimation is described.

The upper side of the equation (10) is multiplied by z1[k], and thelower side of the equation (10) is multiplied by z2[k], to obtain thefollowing equation (51).

$\begin{matrix}{\begin{pmatrix}{z\; {1\lbrack k\rbrack}z\; {1\left\lbrack {k + 1} \right\rbrack}} \\{z\; {2\lbrack k\rbrack}z\; {2\left\lbrack {k + 1} \right\rbrack}}\end{pmatrix} = \begin{pmatrix}{{{c \cdot z}\; {1\lbrack k\rbrack}^{2}} - {{s \cdot z}\; {1\lbrack k\rbrack}z\; {2\lbrack k\rbrack}} + {L\; {4 \cdot z}\; {1\lbrack k\rbrack}{e\lbrack k\rbrack}}} \\{{{s \cdot z}\; {1\lbrack k\rbrack}z\; {2\lbrack k\rbrack}} + {{c \cdot z}\; {2\lbrack k\rbrack}^{2}} - {L\; {5 \cdot z}\; {2\lbrack k\rbrack}{e\lbrack k\rbrack}}}\end{pmatrix}} & (51)\end{matrix}$

In the equation (51), a11 through a22 of the equation (10) aresubstituted by sine and cosine of the equations (9) and (18), and sineand cosine are represented by “s” and “c”, respectively.

By summing up the upper side and the lower side of the equation (51),the following equation (52) is obtained.

z1[k]z1[k+1]+z2[k]z2[k+1]=c(z1[k] ² +z2[k]²)+(L4·z1[k]+L5·z2[k])e[k]  (52)

Based on the equation (52), cos(ωT) (=c) is calculated according to thefollowing equation (53).

$\begin{matrix}{c = {\frac{{{z\; {1\lbrack k\rbrack}z\; {1\left\lbrack {k + 1} \right\rbrack}} + {z\; {2\lbrack k\rbrack}z\; {2\left\lbrack {k + 1} \right\rbrack}}}\;}{{z\; {1\lbrack k\rbrack}^{2}} + {z\; {2\lbrack k\rbrack}^{2}}} - {\frac{{L\; {4 \cdot z}\; {1\lbrack k\rbrack}} + {L\; {5 \cdot z}\; {2\lbrack k\rbrack}}}{{z\; {1\lbrack k\rbrack}^{2}} + {z\; {2\lbrack k\rbrack}^{2}}}{e\lbrack k\rbrack}}}} & (53)\end{matrix}$

The equation (53) is set as the adaptive law of the estimator 24 of FIG.5.

As for the sine and cosine components in a case where a filter is usedas described above, z1[k] and z2[k] of the denominators differ fromthose of the equation of current observers. Also, the numerators of thesecond terms of the right sides of the equations (50) and (53) alsodiffer from those of the equations of current observers, in having z1[k]and z2[k].

As mentioned above, a value of estimated error of sin(ωT) or cos(ωT) iscalculated with ω representing an angular frequency of a disturbance andT representing the sampling period to perform the disturbance adaptivecontrol. Therefore, the estimation accuracy of the disturbance frequencycan be improved, thereby the disturbance adaptive control can berealized with high accuracy.

Although the above position control devices are designed for heads, theposition control device may also be applied to other position controldevices. Likewise, although the disk devices are magnetic disk devicesin the above embodiments, the disk device may also be applied to otherdata storage devices.

The various modules of the systems described herein can be implementedas software applications, hardware and/or software modules, orcomponents on one or more computers, such as servers. While the variousmodules are illustrated separately, they may share some or all of thesame underlying logic or code.

While certain embodiments of the inventions have been described, theseembodiments have been presented by way of example only, and are notintended to limit the scope of the inventions. Indeed, the novel methodsand systems described herein may be embodied in a variety of otherforms; furthermore, various omissions, substitutions and changes in theform of the methods and systems described herein may be made withoutdeparting from the spirit of the inventions. The accompanying claims andtheir equivalents are intended to cover such forms or modifications aswould fall within the scope and spirit of the inventions.

1. A position control apparatus configured to perform position controlon an object with the use of an actuator in accordance with a positionof the object, comprising: a digital control module configured toperform position control including disturbance adaptive control with apredetermined sampling period using a control constant, in accordancewith a position error between a target position and a current positionof the object; and a table configured to store the control constantcorresponding to a value of sin(ωT) or cos(ωT), with ω representing anangular frequency of a disturbance, T representing the sampling period,wherein the digital control module is configured to determine a controlvalue of the actuator in accordance with the position error, calculatesthe value of sin(ωT) or cos(ωT) according to an adaptive law from asignal based on the position error, reads the corresponding controlconstant from the table in accordance with the calculated value ofsin(ωT) or cos(ωT), and updates the control constant, to perform theposition control including the disturbance adaptive control.
 2. Theposition control apparatus of claim 1, wherein the digital controlmodule performs the position control including the disturbance adaptivecontrol through observer control.
 3. The position control apparatus ofclaim 2, wherein the digital control module calculates an error from astate variable of the observer, an estimated gain, and an estimatedposition error, and adds the estimated error to the value of sin(ωT) orcos(ωT), to update the value of sin(ωT) or cos(ωT).
 4. The positioncontrol apparatus of claim 2, wherein the digital control modulecalculates an error from a state variable of a current sample of theobserver and a state variable of a next sample, to update the value ofsin(ωT) or cos(ωT).
 5. The position control apparatus of claim 1,wherein the digital control module performs clipping, so as to restrictthe calculated value of sin(ωT) or cos(ωT) within a predetermined range.6. The position control apparatus of claim 1, wherein the digitalcontrol module includes: a control module configured to calculate thecontrol value of the actuator in accordance with the position error; anda disturbance adaptive control module configured to calculate the valueof sin(ωT) or cos(ωT) according to the adaptive law, and calculate adisturbance adaptive control value with the use of the control constantthat is read from the table in accordance with the calculated value ofsin(ωT) or cos(ωT), and the actuator is driven with the control value ofthe control module and the disturbance adaptive control value.
 7. Theposition control apparatus of claim 2, wherein the table stores a stateestimating gain of the observer corresponding to the estimated value ofsin(ωT) or cos(ωT), and the digital control module updates a stateestimating gain of the observer as the control constant with the use ofa state estimating gain read from the table.
 8. The position controlapparatus of claim 3, wherein the digital control module determines thevalue of sin(ωT) according to the following equations (29) and (30), ordetermines the value of cos(ωT) according to the following equations(31) and (32): $\begin{matrix}{{E\lbrack k\rbrack} = {\frac{{L\; {4 \cdot z}\; {2\left\lbrack {k + 1} \right\rbrack}} - {L\; {5 \cdot z}\; {1\left\lbrack {k + 1} \right\rbrack}}}{{z\; {1\left\lbrack {k + 1} \right\rbrack}^{2}} + {z\; {2\left\lbrack {k + 1} \right\rbrack}^{2}}}{e\lbrack k\rbrack}}} & (29) \\{{\sin \left( {{\omega \left\lbrack {k + 1} \right\rbrack}T} \right)} = {{\sin \left( {{\omega \lbrack k\rbrack}T} \right)} + {K \cdot {E\lbrack k\rbrack}}}} & (30) \\{{E\lbrack k\rbrack} = {{- \frac{{L\; {4 \cdot z}\; {1\left\lbrack {k + 1} \right\rbrack}} + {L\; {5 \cdot z}\; {2\left\lbrack {k + 1} \right\rbrack}}}{{z\; {1\left\lbrack {k + 1} \right\rbrack}^{2}} + {z\; {2\left\lbrack {k + 1} \right\rbrack}^{2}}}}{e\lbrack k\rbrack}}} & (31) \\{{\cos \left( {{\omega \left\lbrack {k + 1} \right\rbrack}T} \right)} = {{\cos \left( {{\omega \lbrack k\rbrack}T} \right)} + {K \cdot {E\lbrack k\rbrack}}}} & (32)\end{matrix}$
 9. The position control apparatus of claim 4, wherein thedigital control module determines the value of sin(ωT) according to thefollowing equations (33) through (35), or determines the value ofcos(ωT) according to the following equations (36) through (38):$\begin{matrix}{{G\lbrack k\rbrack} = \frac{{z\; {1\lbrack k\rbrack}z\; {2\left\lbrack {k + 1} \right\rbrack}} - {z\; {2\lbrack k\rbrack}z\; {1\left\lbrack {k + 1} \right\rbrack}}}{{z\; {1\left\lbrack {k + 1} \right\rbrack}^{2}} + {z\; {2\left\lbrack {k + 1} \right\rbrack}^{2}}}} & (33) \\{{E\lbrack k\rbrack} = {{G\lbrack k\rbrack} - {\sin \left( {{\omega \lbrack k\rbrack}T} \right)}}} & (34) \\{{\sin \left( {{\omega \left\lbrack {k + 1} \right\rbrack}T} \right)} = {{\sin \left( {{\omega \lbrack k\rbrack}T} \right)} + {K \cdot {E\lbrack k\rbrack}}}} & (35) \\{{G\lbrack k\rbrack} = \frac{{z\; {1\lbrack k\rbrack}z\; {1\left\lbrack {k + 1} \right\rbrack}} + {z\; {2\lbrack k\rbrack}z\; {2\left\lbrack {k + 1} \right\rbrack}}}{{z\; {1\left\lbrack {k + 1} \right\rbrack}^{2}} + {z\; {2\left\lbrack {k + 1} \right\rbrack}^{2}}}} & (36) \\{{E\lbrack k\rbrack} = {{G\lbrack k\rbrack} - {\cos \left( {{\omega \lbrack k\rbrack}T} \right)}}} & (37) \\{{\cos \left( {{\omega \left\lbrack {k + 1} \right\rbrack}T} \right)} = {{\cos \left( {{\omega \lbrack k\rbrack}T} \right)} + {K \cdot {E\lbrack k\rbrack}}}} & (38)\end{matrix}$
 10. A disk apparatus comprising: a head configured to readinformation from a disk; an actuator configured to move the head in atransverse direction of tracks of the disk; a digital control moduleconfigured to perform position control including disturbance adaptivecontrol with a predetermined sampling period using a control constant,in accordance with a position error between a target position and acurrent position of the object; and a table configured to store thecontrol constant corresponding to a value of sin(ωT) or cos(ωT), with ωrepresenting an angular frequency of a disturbance, T representing thesampling period, wherein the digital control module is configured todetermine a control value of the actuator in accordance with theposition error, calculates the value of sin(ωT) or cos(ωT) according toan adaptive law from a signal based on the position error, reads thecorresponding control constant from the table in accordance with thecalculated value of sin(ωT) or cos(ωT), and updates the controlconstant, to perform the position control including the disturbanceadaptive control.
 11. The disk apparatus of claim 10, wherein thedigital control module performs the position control including thedisturbance adaptive control through observer control.
 12. The diskapparatus of claim 11, wherein the digital control module calculates anerror from a state variable of the observer, an estimated gain, and anestimated position error, and adds the estimated error to the value ofsin(ωT) or cos(ωT), to update the value of sin(ωT) or cos(ωT).
 13. Thedisk apparatus of claim 11, wherein the digital control modulecalculates an error from a state variable of a current sample of theobserver and a state variable of a next sample, to update the value ofsin(ωT) or cos(ωT).
 14. The disk apparatus of claim 10, wherein thedigital control module performs clipping, so as to restrict thecalculated value of sin(ωT) or cos(ωT) within a predetermined range. 15.The disk apparatus of claim 10r wherein the digital control moduleincludes: a control module configured to calculate the control value ofthe actuator in accordance with the position error; and a disturbanceadaptive control module configured to calculate the value of sin(ωT) orcos(ωT) according to the adaptive law, and calculate a disturbanceadaptive control value with the use of the control constant that is readfrom the table in accordance with the calculated value of sin(ωT) orcos(ωT), and the actuator is driven with the control value of thecontrol module and the disturbance adaptive control value.
 16. The diskapparatus of claim 11, wherein the table stores a state estimating gainof the observer corresponding to the estimated value of sin(ωT) orcos(ωT), and the digital control module updates a state estimating gainof the observer as the control constant with the use of a stateestimating gain read from the table.
 17. The disk apparatus of claim 12,wherein the digital control module determines the value of sin(ωT)according to the following equations (29) and (30), or determines thevalue of cos(ωT) according to the following equations (31) and (32):$\begin{matrix}{{E\lbrack k\rbrack} = {\frac{{L\; {4 \cdot z}\; {2\left\lbrack {k + 1} \right\rbrack}} - {L\; {5 \cdot z}\; {1\left\lbrack {k + 1} \right\rbrack}}}{{z\; {1\left\lbrack {k + 1} \right\rbrack}^{2}} + {z\; {2\left\lbrack {k + 1} \right\rbrack}^{2}}}{e\lbrack k\rbrack}}} & (29) \\{{\sin \left( {{\omega \left\lbrack {k + 1} \right\rbrack}T} \right)} = {{\sin \left( {{\omega \lbrack k\rbrack}T} \right)} + {K \cdot {E\lbrack k\rbrack}}}} & (30) \\{{E\lbrack k\rbrack} = {{- \frac{{L\; {4 \cdot z}\; {1\left\lbrack {k + 1} \right\rbrack}} + {L\; {5 \cdot z}\; {2\left\lbrack {k + 1} \right\rbrack}}}{{z\; {1\left\lbrack {k + 1} \right\rbrack}^{2}} + {z\; {2\left\lbrack {k + 1} \right\rbrack}^{2}}}}{e\lbrack k\rbrack}}} & (31) \\{{\cos \left( {{\omega \left\lbrack {k + 1} \right\rbrack}T} \right)} = {{\cos \left( {{\omega \lbrack k\rbrack}T} \right)} + {K \cdot {E\lbrack k\rbrack}}}} & (32)\end{matrix}$
 18. The disk apparatus of claim 13, wherein the digitalcontrol module determines the value of sin(ωT) according to thefollowing equations (33) through (35), or determines the value ofcos(ωT) according to the following equations (36) through (38):$\begin{matrix}{{G\lbrack k\rbrack} = \frac{{z\; {1\lbrack k\rbrack}z\; {2\left\lbrack {k + 1} \right\rbrack}} - {z\; {2\lbrack k\rbrack}z\; {1\left\lbrack {k + 1} \right\rbrack}}}{{z\; {1\left\lbrack {k + 1} \right\rbrack}^{2}} + {z\; {2\left\lbrack {k + 1} \right\rbrack}^{2}}}} & (33) \\{{E\lbrack k\rbrack} = {{G\lbrack k\rbrack} - {\sin \left( {{\omega \lbrack k\rbrack}T} \right)}}} & (34) \\{{\sin \left( {{\omega \left\lbrack {k + 1} \right\rbrack}T} \right)} = {{\sin \left( {{\omega \lbrack k\rbrack}T} \right)} + {K \cdot {E\lbrack k\rbrack}}}} & (35) \\{{G\lbrack k\rbrack} = \frac{{z\; {1\lbrack k\rbrack}z\; {1\left\lbrack {k + 1} \right\rbrack}} + {z\; {2\lbrack k\rbrack}z\; {2\left\lbrack {k + 1} \right\rbrack}}}{{z\; {1\left\lbrack {k + 1} \right\rbrack}^{2}} + {z\; {2\left\lbrack {k + 1} \right\rbrack}^{2}}}} & (36) \\{{E\lbrack k\rbrack} = {{G\lbrack k\rbrack} - {\cos \left( {{\omega \lbrack k\rbrack}T} \right)}}} & (37) \\{{\cos \left( {{\omega \left\lbrack {k + 1} \right\rbrack}T} \right)} = {{\cos \left( {{\omega \lbrack k\rbrack}T} \right)} + {K \cdot {E\lbrack k\rbrack}}}} & (38)\end{matrix}$